The present invention relates to methods and apparatus for the control of dynamic systems. More particularly, the present invention relates to methods and apparatus for controlling dynamic systems exhibiting non-minimum phase behavior.
There has recently been much interest in the development of methods and techniques for controlling complex dynamic systems. Dynamic systems having non-minimum phase behavior are examples of one type of such complex systems. Non-minimum phase behavior is a term used in the art to describe certain types of frequency domain transfer functions relating system inputs to system outputs. Such non-minimum phase behavior is typical of distributed parameter systems. Transportation lag or pure time delay between an input signal and its corresponding output is another form of non-minimum phase behavior. Non-minimum phase behavior is also exhibited by systems in which an input produces an initial negative response in the system output, with a subsequent change of sign and approach of the output to its positive asymptote. An example of one type of this non-minimum phase behavior is often called "shrink-swell" behavior by operators of such systems. Such shrink-swell behavior is usually associated with systems whose transfer functions contain right half plane zeros.
The control of water level in the secondary loop of a nuclear steam supply system is difficult because the system behaves with non-minimum phase dynamics. Changes in reactor power, steam flow, feedwater temperature and feedwater flow all affect the measured level in the steam generator. The level controller in such a system maintains the level in the steam drum on target and within limits by changing feedwater flow to compensate for the changes in level produced by other factors. In systems exhibiting non-minimum phase behavior, the system cannot be easily controlled by simple feedback of the error level. For example, if the feedwater controller in a nuclear steam supply system responds only to existing level error, the system can become unstable. Because of the long lag times in such systems, controller responses which are made only after a disturbance in level has occurred are not likely to produce an effect on level in time to avoid crossing a limit. The classical approach to this problem is to speed up controller response by adding derivative action to the controller. Frequently, however, such an approach can result in unstable control for systems having non-minimum phase dynamics. More particularly, in a " shrink and swell" system the control action that ultimately brings the system back into balance is the same action which initially exacerbates the problem. As a result, derivative action will generally result in unstable control.
For systems having complex dynamics, controller performance can be dramatically improved by providing information that helps the controller anticipate output behavior. In many such systems, however, prediction of the system behavior is difficult because access to the critical state variables of the system is not generally available. For example, in nuclear power plant steam supply systems, accurate measures of steam flow and feed water flow are not generally available at low power rates. As a result, the controller generally has no direct way of knowing whether steam flow and feedwater flow are in balance and how much of a change in feedwater flow is required to bring them into balance. Reliance is placed almost exclusively on level trend to infer this information. Because of the long lags and shrink and swell effects previously discussed, there is significant delay before information about the feed flow/steam flow balance is manifested in level behavior.
Several control methods have heretofore used such predictive information to mprove controller performance. One method for developing such information, sometimes referred to as "quickened display", combines current parameter error with velocity and even acceleration information in a single display element. See for example "Man-Machine Systems:Information, Control, and Decision Models of Human Performance", MIT Press, 1974, by Thomas B. Sheridan and William R. Ferrell, at pages 268-270. Because the velocity is combined with the current value of the parameter, the quickened display indicates where the controlled parameter is likely to be if no control action is taken. It should be noted, however, that these predictions are based upon recent past performance of the system and not the intrinsic dynamics of the system.
Other control methods, known as simulation based control, use predictive information to explicitly project the future value or trajectory of the controlled parameter. See for example Man-Machine Systems, supra, at 271-273. In this method, a computer simulation of the system is run faster than real time to generate a projection of parametric behavior. This type of prediction is subject to increasing error as the projection moves further from the current data. Simulation based control such as this is also subject to error based on discrepancies between the dynamic model of the system and the actual plant dynamics. The use of such control methods is severely limited because of these two types of errors and because of the expense and technical limitations of running sufficiently valid models faster than real time. Even if these disadvantages were to be overcome, methods such as this would be unsatisfactory for systems with rate integration dynamics or unstable right half plane poles since the errors in such systems increase without bounds when prediction is based upon such methods.
The use of fast time model based information to aid in the control of steam generator level in a nuclear power plant has been suggested by Venhuizen, J. R. and Griffith, J. M. in their article entitled "Predictor Display Concepts for Use in Nuclear Power Plant Control", National Technical Information Service, 1983. It is suggested that a predictor could be developed through Kalman filter techniques for estimating the state of a linear system. Even with accurate state information via a Kalman filter, fast time simulation techniques produce unacceptable error behavior for systems with rate integration or unstable dynamics. Moreover, the fast time simulation approach does nothing to alleviate the difficulty of controlling non-minimum phase systems.